Finite Group Databasebeta

C2×#13114847 #15862373

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13114847

Splittings

FittingC22×C13×C4⋊C8 ⋊ C2
SylowC13 ⋊ C2×#1804

Subgroups

subgroupG/H
centerC24C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×C4⋊C8C2
socleC24×C13C2×D4
prime radicalC23×D52C22
cosocleC22×C4×C13C24
hypercenterC22×C4⋊C8D13
hypocenterC13C2×#1804
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

1942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 169022);